Let \(F/\mathbb {F}_q\)  be a function field with genus \(g\)  over the full constant field \(\mathbb {F}_q\) . Let \(\mathbb {P}_F\)  denote the set of places of \(F\) . Any place of \(F\)  with degree one is called rational.
For a divisor \(G\)  of function field \(F/\mathbb {F}_q\) , we define the Riemann-Roch space by
\(\mathcal {L}(G):=\lbrace u\in F^*:\; (u)+G\geqslant 0\rbrace \cup \lbrace 0\rbrace .\) 
From Riemann's theorem, \(\mathcal {L}(G)\)  is a finite-dimensional vector space over \(\mathbb {F}_q\)  and its dimension \(\ell (G)\)  is lower bounded by \(\ell (G)\geqslant \deg (G)-g+1\) . Moreover, the equality holds true if \(\deg (G)\geqslant 2g-1\)  from [1]}.
